Computational Complexity of the Recoverable Robust Shortest Path Problem with Discrete Recourse

TL;DR

This paper analyzes the computational complexity of the recoverable robust shortest path problem under discrete uncertainty, establishing its high-level hardness results and the complexity of related adversarial problems.

Contribution

It strengthens existing complexity results by proving Sigma_3^p-hardness and Pi_2^p-hardness for key variants of the problem and its inner adversarial component.

Findings

The problem is Sigma_3^p-hard for arc exclusion and symmetric difference neighborhoods.

The inner adversarial problem is Pi_2^p-hard for these neighborhoods.

Complexity results are extended for the recoverable robust shortest path problem with discrete uncertainty.

Abstract

In this paper the recoverable robust shortest path problem is investigated. Discrete budgeted interval uncertainty representation is used to model uncertain second-stage arc costs. The known complexity results for this problem are strengthened. It is shown that it is Sigma_3^p-hard for the arc exclusion and the arc symmetric difference neighborhoods. Furthermore, it is also proven that the inner adversarial problem for these neighborhoods is Pi_2^p-hard.